CORRELATION MODELS FOR CHILDHOOD EPIDEMICS

One of the simplest set of equations for the description of epidemics (the SEIR equations) has been much studied, and produces reasonable ap proximations to the dynamics of communicable disease. However, it has long been recognized that spatial and social structure are important i f we are to understand the long-term persistence and detailed behaviou r of disease. We will introduce three pair models which attempt to cap ture the underlying heterogeneous structure by studying the connection s and correlations between individuals. Although modelling the correla tions necessarily leads to more complex equations, this pair formulati on naturally incorporates the local dynamical behaviour generating mor e realistic persistence. In common with other studies on childhood dis eases we will focus our attention on measles, for which the case retur ns are particularly well documented and long running.